Robustness of square networks

The topic of security often enters in many real world situations. In this paper we focus on security of networks on which it is based the delivery of services and goods (e.g. water and electric supply networks) the transfer of data (e.g. web and telecommunication networks), the movement of transport means (e.g. road networks), etc... We use a fluid dynamic framework, networks are described by nodes and lines and our analysis starts from an equilibrium status: the flows are constant in time and along the lines. When a failure occurs in the network a shunt changes the topology of the network and the flows adapt to it reaching a new equilibrium status. The question we consider is the following: is the new equilibrium satisfactory in terms of achieved quality standards? We essentially individuate, for regular square networks, the nodes whose breakage compromises the quality of the flows. It comes out that networks which allow circular flows are the most robust with respect to damages.